My book says
... But the threshold voltage are much higher and slightly different for each color. The reverse breakdown voltages of LEDs are very low.
While I understand that the reverse breakdown voltage should be low because of the heavy doping, but I do not understand reason for high threshold voltage.
I know that the band gap should be higher because the wavelength of the light emitted needs to be smaller. So does band gap have any relation with the threshold voltage?
Edit: I found out that barrier potential depends on the negative logarithm of \$n_i\$ and so does the band gap